This diagram represents a neuron with two dendritic branches off the Soma. The "x"'s are meant to represent where a synapse has been placed on along the dendritic tree. The "===<" structure is meant to represent the axon.

If a strong EPSP reaches synapse "x1", as it travels along the dendritic stalk it must have to pass "x2" through "x5" before it reaches the "O" Soma to test for being able to further pass the axon hillock.

This question is about AMPA and NMDA receptor action for LTP (see: sumanasinc.com/webcontent/animations/content/receptors.html for a flash animation describing the general action). Presumably, this receptor activity can strengthen a synapse for up to several weeks and is therefore thought to aid the process of memory formation.

What I'd like to know is how many synapses end up becoming strengthened from intense activity (such as "bursting" rather than "tonic" signaling) at just one synapse?

When an EPSP is generated in "x1", wont this also open NMDA receptors along the way to the Soma, in the synapses it passes as the EPSP is propagating toward the cell? The signal degrades on the way down, but wont at least "x2" also recieve a high EPSP and open up its NMDA channel?

And wouldn't this therefore mean that the following statement is correct: The closer a synapse is to neighboring synapses that share a common dendritic branch, the more it will indirectly become strengthened from LTP-inducing activity going on in its nearest synapses, to a Gaussian degree.

I guess the crux of this question lies on whether or not the receptors that are stored in dendrites can receive ion flow that arrives from stalk-to-spine in addition to regular axon-dendritic signal communication.

This seems like simple question to ask on this matter, but for the life of me I've found no data to address this particular issue with absolute clarity. In terms of plasticity and memory, it would suggest that the plastic organization of synapses along a dendritic stalk is a critical variable in favoring particular groups of synaptic evidence, rather than just individual synapses.

Anyway, if anyone is interested in this question but doesn't have an answer, here at least is another good place to visit for more information: thebrain.mcgill.ca/flash/i/i_07/i_07_m/i_07_m_tra/i_07_m_tra.html

I ask this question here because I've found no resources that go into the depth I'm interested in on this topic.

Also, one more basic question I've had trouble getting answered: if a strong enough signal arrives at synapse "x5", could the EPSP travel along paths that are not directly toward the axon hillock? For instance, could the EPSP from "x5" travel distally away from the Cell all the way to "x1"? Could the EPSP (or IPSP for that matter) travel to the Cell, and then up a different dendritic branch as well as into the axon hillock? In the above diagram, this question is asking if a signal could travel from "x5" to "x7", or even make it all the way to "x6".

[update]
After writing this question, I did find this on Wikipedia:
"Spines are particularly advantageous to neurons by compartmentalizing signals; a signal delivered to one spine effects only the recipient spine and not the entire neuron. They thus localize synaptic signaling by forming biochemical compartments that can encode changes in the state of an individual synapse without necessarily affecting the state of other synapses of the same neuron. This compartmentalization arises from the restriction of diffusion of ions and second messengers from the spine to the dendritic stalk."

But it doesn't link to a more in depth explanation, or explain the mechanism by which spine-to-stalk ion flow is supposedly so uniformly one-way in all types of neurons.

Excellent sleuth work, Cincinnatus :) It took me a bit to find myself a copy of the paper, but I managed to and it addresses all these questions and more admirably. I thank you very much for your spot-on reply.